From Chaos to Order - Trading Regime Transitions with Lyapunov–Hurst Signals

Price dynamics can alternate between chaotic and orderly phases. When a system’s largest Lyapunov exponent drops and the correlation dimension compresses, trajectories become more predictable—often coinciding with trendable structure. Pairing this with a simple trend filter and Hurst exponent provides a compact framework to trade regime transitions rather than raw noise.

Signal Architecture

• Chaos Metrics (rolling on returns): Largest Lyapunov exponent (instability), correlation dimension (attractor complexity), and Hurst exponent (persistence vs. mean reversion).
• Regime switch trigger: Transition from chaotic → ordered (Lyapunov falls below threshold and corr-dim low). Go long if price is above trend; short if below.
• Fail-safe exits: Exit on a renewed chaotic surge (Lyapunov well above threshold) or when Hurst signals a contrary regime without trend alignment.
• Risk control: A hard stop is attached at entry (percentage-based), canceled/updated on closes and flips.

Main Strategy Logic (decision loop only)

def next(self):
    if self.order is not None:
        return

    # accumulate rolling returns
    if not np.isnan(self.returns[0]):
        self.returns_history.append(self.returns[0])
    if len(self.returns_history) > self.p.lookback * 2:
        self.returns_history = self.returns_history[-self.p.lookback * 2:]

    # need enough history
    if len(self.returns_history) < self.p.lookback:
        return

    # compute chaos metrics on the latest window
    recent = np.array(self.returns_history[-self.p.lookback:])
    lyap, corr_dim, hurst = self.analyze_strange_attractor(recent)

    # track previous regime state
    prev_lyap = self.lyapunov_exponent
    self.lyapunov_exponent = lyap
    self.correlation_dimension = corr_dim
    self.hurst_exponent = hurst

    # trade only on transitions into "order" with trend alignment
    long_setup = (lyap < self.p.lyap_threshold and prev_lyap >= self.p.lyap_threshold
                  and corr_dim < self.p.corr_dim_threshold
                  and self.data.close[0] > self.trend_ma[0])

    short_setup = (lyap < self.p.lyap_threshold and prev_lyap >= self.p.lyap_threshold
                   and corr_dim < self.p.corr_dim_threshold
                   and self.data.close[0] < self.trend_ma[0])

    # exits on renewed chaos
    chaos_exit = (lyap > self.p.lyap_threshold * 2 and self.position)

    # alternative thrust: Hurst persistence gates with trend
    hurst_long = (hurst > 0.6 and self.data.close[0] > self.trend_ma[0] and not self.position)
    hurst_short = (hurst < 0.4 and self.data.close[0] < self.trend_ma[0] and not self.position)

    # execute
    if long_setup:
        if self.position.size < 0 and self.stop_order: self.cancel(self.stop_order)
        self.order = self.close() if self.position.size < 0 else self.buy()

    elif short_setup:
        if self.position.size > 0 and self.stop_order: self.cancel(self.stop_order)
        self.order = self.close() if self.position.size > 0 else self.sell()

    elif chaos_exit:
        if self.stop_order: self.cancel(self.stop_order)
        self.order = self.close()

    elif hurst_long:
        self.order = self.buy()

    elif hurst_short:
        self.order = self.sell()

Why it Works

• Structure over noise: Trades the transition into lower-dimensional, lower-instability regimes where path-dependence weakens and trends persist.
• Orthogonal filters: Lyapunov (instability), correlation dimension (complexity), and Hurst (serial dependence) supply complementary signals.
• Contextual trend gate: A simple moving average avoids counter-trend fading of chaos.

Tuning Notes

• Raise lyap_threshold to demand cleaner order and fewer trades in choppy assets.
• Tighten corr_dim_threshold to isolate simpler attractors; loosen to participate more.
• Adjust trend_period to match the instrument’s dominant cycle.
• Consider replacing the fixed stop with ATR-based distance to normalize risk across regimes.

Backtest Results (DOGE-USD, 2018–2025, 12-month rolling windows)

strategy = load_strategy("ChaosStrategy")
    
ticker = "DOGE-USD"
start = "2018-01-01"
end = "2025-01-01"
window_months = 12

df = run_rolling_backtest(ticker=ticker, start=start, end=end, window_months=window_months)

• Mean Return % per window: 52.85%
• Median Return % per window: 16.08%
• Std Dev % per window: 64.76%
• Min / Max per window: -16.39% / 175.12%
• Sharpe Ratio per window: 0.82
• Total Return (whole backtest): +992.23%
• Max Drawdown (whole backtest): -16.39%
• Win Rate: 85.71%
• Total-period Sharpe Ratio: 0.87

Interpretation: The chaos–order regime framework achieved high total returns with a strong win rate and modest drawdowns relative to crypto’s inherent volatility. The strategy excelled in strong trending regimes (175% peak window gain) but also showed periods of muted performance when regime shifts were less distinct. This suggests the model’s edge is concentrated in high-persistence structural transitions—exactly where chaos theory predicts the largest predictability boost.